Minimum revenue guarantees valuation in PPP projects under a mean reverting process

Minimum revenue guarantees, where the government assumes a portion of the traffic risk to guarantee a minimum level of revenue and profitability to the investors, is a standard risk mitigation mechanism for Public-Private Partnership contracts. Typically, valuation models for these guarantees assume that traffic volume follows a geometric Brownian motion under the Real Options Approach. However, this is often done without testing whether this assumption is reasonable or not. In this article, statistical tests are applied to check the validity of this assumption and show how toll road traffic can be modelled under alternate models, such as Mean Reverting processes, if the geometric Brownian motion assumption is rejected. In that sense, this approach is applied to the case of a toll road concession in Colombia where a Mean Reverting process is used to model the traffic. Finally, it is showed that this model is a valid tool for defining the fair value of the minimum amount of revenue secured by the government.